When two mirrors are placed at an angle of 90º to each other, how many images will be formed when an object is placed in front of the mirrors

Analysis

The question asks for the number of images formed when an object is placed between two plane mirrors inclined at a specific angle ($\theta = 90^\circ$).

Concept

When two plane mirrors are inclined at an angle $\theta$, the number of images ($n$) formed is determined by the formula:

This formula is used when the result of $\frac{360^\circ}{\theta}$ is an even integer. If the result is an odd integer, the formula remains the same if the object is placed asymmetrically, but if the object is placed symmetrically, the number of images is $\frac{360^\circ}{\theta} - 1$. However, for a $90^\circ$ angle, the calculation is straightforward.

Solution

1. Identify the given angle: $\theta = 90^\circ$
2. Calculate the ratio: $$\frac{360^\circ}{90^\circ} = 4$$
3. Apply the formula: Since 4 is an even number, we subtract 1 to account for the overlapping images: $$n = 4 - 1 = 3$$

Therefore, 3 images will be formed.

Conclusion

The correct option is C.

Exam Tip

A quick way to remember this is the "Even-Odd Rule":

• If $\frac{360}{\theta}$ is even, the number of images is $\frac{360}{\theta} - 1$.
• If $\frac{360}{\theta}$ is odd, the number of images is $\frac{360}{\theta} - 1$ (for symmetric placement) or simply $\frac{360}{\theta}$ (for asymmetric placement).
• If $\frac{360}{\theta}$ is a fraction, the number of images is the integer part of the result.